I don't know how to start with these problems. Please some guidance.
A food processing company employs sorters to pick out the premium quality apples from a conveyor belt and pack them into cartons, whilst letting the standard quality apples continue on to a large juicer. Because of the speed at which the sorting is done some mistakes do occur. Occasional quality audits suggest that 6% of the apples picked out and packed as premium were only of standard quality. The cartons contain 4 layers, each
containing 24 apples.
a) A shift supervisor team samples a layer of 24 apples packed by sorter X, and finds that 3 are standard quality. Determine the probability of getting 3 or more standard apples in a layer of 24, and explain what this suggests about sorter X. State any assumptions that you may need to make.
b) To check their suspicions from part (a), the supervisor looks at a whole carton packed by sorter X. They find that it contained 12 standard quality apples out of 96. Determine the approximate probability of 12 or more of 96 apples being of standard quality, and explain whether this is consistent with your conclusion in part(a).
c) Apples arrive at the sorting station at a rate of 2160 per hour. When a carton is full, it takes 2 seconds for the sorter to grab another carton and be ready to continue sorting. Determine the probability that no apples pass by their sorting station during the time it takes to grab another carton. Be careful to state any assumptions that you need to make.
d) Determine the probability that more than 2 apples are missed during the changeover period.